Testing ΛCDM with the growth function δ(a): Current constraints

We have compiled a data set consisting of 22 data points at a redshift range (0.15, 3.8) which can be used to constrain the linear perturbation growth rate f=(dln⁡δ)/(dln⁡a). Five of these data points constrain directly the growth rate f through either redshift distortions or change of the power spectrum with redshift. The rest of the data points constrain f indirectly through the rms mass fluctuation σ₈(z) inferred from L_y-α at various redshifts. Our analysis tests the consistency of the ΛCDM model and leads to a constraint of the Wang-Steinhardt growth index γ [defined from f=Ω_m(a)^γ] as γ=0.67_-0.17^+0.20. This result is clearly consistent at 1σ with the value γ=(6)/(11)=0.545 predicted by ΛCDM. We also apply our analysis on a new null test of ΛCDM which is similar to the one recently proposed by Chiba and Nakamura (arXiv:0708.3877) but does not involve derivatives of the expansion rate H(z). This also leads to the fact that ΛCDM provides an excellent fit to the current linear growth data.